Chapter 12.7, Problem 24PPS

To determine

The probability at least 10 of the polled students did not want to go to a college.

Answer to Problem 24PPS

The probability is 0.9778.

Explanation of Solution

Given:

Jacqui’s school determined that 88% of the students wanted to go to a college. Jacqui surveyed 150 random students from the school.

Evaluating the standard deviation:

  $\begin{array}{l}\sigma =\sqrt{nsf}\\ =\sqrt{150\cdot 0.88\cdot 0.12}\\ =3.98\end{array}$

The z-score for x=10 is

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ =\frac{10-18}{3.98}\\ =-2.01\end{array}$

Hence, the probability that at least 10 of the polled students did not want to go to college is

  $\begin{array}{l}P\left(x\ge 10\right)=1-P\left(x\le 10\right)\\ =1-P\left(z\le -2.01\right)\\ =1-0.0222\\ =0.9778\end{array}$

Hence , required probability is 0.9778.